case study questions class 12 maths cbse chapter wise pdf

Class 12 Maths: Case Study Based Questions PDF Download

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You must practice some good Case Study questions of Class 12 Maths to boost your preparation to score 95+% on Boards. In this post, you will get Case Study Questions of All Chapters which will come in CBSE Class 12 Maths Board Exams.

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We have provided here Case Study questions for the Class 12 Maths exams. You can read these chapter-wise Case Study questions. Prepared by subject experts and experienced teachers. The answer key is also provided so that you can check the correct answer for each question. Practice these questions to score well in your Board Final exams.

We are providing Case Study questions for class 12 Biology based on the latest syllabi. There is a total of 13 chapters included in CBSE class 12 Maths exams. Students can practice these questions for concept clarity and score better marks in their exams.

Table of Contents

CBSE Class 12th – MATHS : Chapterwise Case Study Question & Solution

CBSE will ask two Case Study Questions in the CBSE class 12 maths questions paper. Question numbers 15 and 16 are case-based questions where 5 MCQs will be asked based on a paragraph. Each theme will have five questions and students will have a choice to attempt any four of them.

Case Study Based Questions for Class 12 Maths

Class 12 Physics Case Study Questions Class 12 Chemistry Case Study Questions Class 12 Biology Case Study Questions Class 12 Maths Case Study Questions

Books for Class 12 Maths

Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 12 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 12th.

Class 12 Maths Syllabus 2022-23

Unit-i: relations and functions.

1. Relations and Functions (15 Periods)

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

2. Inverse Trigonometric Functions (15 Periods)

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices (25 Periods)

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Oncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants 25 Periods

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III: Calculus

1. Continuity and Differentiability (20 Periods)

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin −1  𝑥 , cos −1  𝑥 and tan −1  𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

2. Applications of Derivatives (10 Periods)

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

3. Integrals (20 Periods)

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals (15 Periods)

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

5. Differential Equations (15 Periods)

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors (15 Periods)

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

2. Three – dimensional Geometry (15 Periods)

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit-V: Linear Programming

1. Linear Programming (20 Periods)

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

1. Probability 30 (Periods)

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

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Case Study Questions for Class 12 Maths PDF Download

We have provided here Case Study questions for the Class 12 Maths for board exams. You can read these chapter-wise Case Study questions. These questions are prepared by subject experts and experienced teachers. The answer key is also provided so that you can check the correct answer for each question. Practice these questions to score well in your final exams.

CBSE 12th Standard CBSE Maths question papers, important notes, study materials, Previous Year questions, Syllabus, and exam patterns. Free 12th Standard CBSE Maths books and syllabus online. Important keywords, Case Study Questions, and Solutions.

Class 12 Maths Case Study Questions

CBSE Class 12 Maths question paper will have case study questions too. These case-based questions will be objective type in nature. So, Class 12 Maths students must prepare themselves for such questions. First of all, you should study NCERT Textbooks line by line, and then you should practice as many questions as possible.

Chapter-wise Solved Case Study Questions for Class 12 Maths

Class 12 students should go through important Case Study problems for Maths before the exams. This will help them to understand the type of Case Study questions that can be asked in Grade 12 Maths examinations. Our expert faculty for standard 12 Maths have designed these questions based on the trend of questions that have been asked in last year’s exams. The solutions have been designed in a manner to help the grade 12 students understand the concepts and also easy to learn solutions.

Books for Class 12 Maths

Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 12 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 12th.

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Class 12 Maths Case Study Questions

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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Class 12 Maths question paper will have 1-2 Case Study Questions. These questions will carry 5 MCQs and students will attempt any four of them. As all of these are only MCQs, it is easy to score good marks with a little practice. Class 12 Maths Case Study Questions are available on the myCBSEguide App and Student Dashboard .

Why Case Studies in CBSE Syllabus?

CBSE has introduced case study questions in the CBSE curriculum recently. The purpose was to make students ready to face real-life challenges with the knowledge acquired in their classrooms. It means, there was a need to connect theories with practicals. Whatsoever the students are learning, they must know how to apply it in their day-to-day life. That’s why CBSE is emphasizing case studies and competency-based education .

Case Study Questions in Maths

Let’s have a look over the class 12 Mathematics sample question paper issued by CBSE, New Delhi. Question numbers 17 and 18 are case study questions.

Focus on concepts

If you go through each MCQ there, you will find that the theme/case study is common but the questions are based on different concepts related to the theme. It means, that if you have done ample practice on the various concepts, you can solve all these MCQs in minutes.

Easy Questions with a Practical Approach

The difficulty level of the questions is average or say easy in some cases. On the other hand, you get four options to choose from. So, you get two levels of support to get full marks with very little effort.

Practice Questions Regularly

Most of the time we feel that it’s easy and neglect it. But in the end, we have to pay for this negligence. This may happen here too. Although it’s easy to score good marks on the case study questions if you don’t practice such questions, you may lose your marks. So, we suggest students should practice at least 30-40 such questions before writing the board exam.

12 Maths Case-Based Questions

We are giving you some examples of case study questions here. We have arranged hundreds of such questions chapter-wise on the myCBSEguide App. It is the complete guide for CBSE students. You can download the myCBSEguide App and get more case study questions there.

Case Study Question – 1

• A is a diagonal matrix
• A is a scalar matrix
• A is a zero matrix
• A is a square matrix
• If A and B are two matrices such that AB = B and BA = A, then B 2 is equal to

Case Study Question – 2

• 4(x 3  – 24x 2   + 144x)
• 4(x 3 – 34x 2   + 244x)
• x 3  – 24x 2   + 144x
• 4x 3  – 24x 2   + 144x
• Local maxima at x = c 1
• Local minima at x = c 1
• Neither maxima nor minima at x = c 1
• None of these

Case Study Questions Matrices -1

Answer Key:

Case Study Questions Matrices – 2

Read the case study carefully and answer any four out of the following questions: Once a mathematics teacher drew a triangle ABC on the blackboard. Now he asked Jose,” If I increase AB by 11 cm and decrease the side BC by 11 cm, then what type of triangle it would be?” Jose said, “It will become an equilateral triangle.”

Again teacher asked Suraj,” If I multiply the side AB by 4 then what will be the relation of this with side AC?” Suraj said it will be 10 cm more than the three times AC.

Find the sides of the triangle using the matrix method and  answer the following questions:

• (a) 3  ×  3

Case Study Questions Determinants – 01

DETERMINANTS:  A determinant is a square array of numbers (written within a pair of vertical lines) that represents a certain sum of products. We can solve a system of equations using determinants, but it becomes very tedious for large systems. We will only do 2 × 2 and 3 × 3 systems using determinants. Using the properties of determinants solve the problem given below and answer the questions that follow:

Three shopkeepers Ram Lal, Shyam Lal, and Ghansham are using polythene bags, handmade bags (prepared by prisoners), and newspaper envelopes as carrying bags. It is found that the shopkeepers Ram Lal, Shyam Lal, and Ghansham are using (20,30,40), (30,40,20), and (40,20,30) polythene bags, handmade bags, and newspapers envelopes respectively. The shopkeeper’s Ram Lal, Shyam Lal, and Ghansham spent ₹250, ₹270, and ₹200 on these carry bags respectively.

• (b) Shyam Lal
• (a) Ram Lal

Case Study Questions Determinants – 02

Case study questions application of derivatives.

• R(x) = -x 2  + 200x + 150000
• R(x) = x 2  – 200x – 140000
• R(x) = 200x 2  + x + 150000
• R(x) = -x 2  + 100 x + 100000
• R'(x) > 0
• R'(x) < 0
• R”(x) = 0
• (a) -x 2  + 200x + 150000
• (a) R'(x) = 0
• (c) 257, -63

Case Study Questions Vector Algebra

• tan−1⁡(5/12)
• tan−1⁡(12/3)
• (b) 130 m/s
• (a)  tan−1⁡(5/12)
• (b) 170 m/s

More Case Study Questions

These are only some samples. If you wish to get more case study questions for CBSE class 12 maths, install the myCBSEguide App. It has class 12 Maths chapter-wise case studies with solutions.

12 Maths Exam pattern

Question Paper Design of CBSE class 12 maths is as below. It clearly shows that 20% weightage will be given to HOTS questions. Whereas 55% of questions will be easy to solve.

• No. chapter-wise weightage. Care to be taken to cover all the chapters
• Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections

12 Maths Prescribed Books

• Mathematics Part I – Textbook for Class XII, NCERT Publication
• Mathematics Part II – Textbook for Class XII, NCERT Publication
• Mathematics Exemplar Problem for Class XII, Published by NCERT
• Mathematics Lab Manual class XII, published by NCERT

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CBSE 12th Standard Maths Subject Case Study Questions with Solutions

By QB365 on 20 May, 2021

QB365 Provides the updated CASE Study Questions for Class 12 , and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

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MTG ScoreMore Case Study Chapter-wise Practice Questions Mathematics Class-12 comprises of over 550 Chapter-wise questions and solutions related to Case study/ Passage based and Assertion & Reason based on latest pattern of CBSE (2020-2021). The Book is designed to measure critical thinking ability and hike up the problem-solving skills of the students.

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MTG ScoreMore Case Study Based Sample Questions Mathematics Class 12 is specially designed to help students get familiar with solving these new patterns of questions. The book covers 550 + sample questions for practice with detailed explanations to each question. Practising these questions will definitely help students to get an edge in their CBSE preparations.

For the academic year 2020-21 CBSE has incorporated more Objective type/MCQ based questions which will focus on measuring critical thinking ability of students. The questions will be focusing on sharpening the problem-solving ability of students.

The new pattern of questions includes Case study based questions, Passage based questions. In Case study based/ Passage based questions, students will be expected to answer questions after reading a given paragraph or a passage.

• 1. Relations and Functions
• 2. Inverse Trigonometric Functions*
• 3. Matrices
• 4. Determinants
• 5. Continuity and Differentiability
• 6. Application of Derivatives
• 7. Integrals*
• 8. Application of Integrals
• 9. Differential Equations
• 10. Vector Algebra
• 11. Three Dimensional Geometry
• 12. Linear Programming
• 13. Probability
• *Case study is not possible in the chapter

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CBSE Case Study Questions for Class 12 Maths Matrices Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Matrices  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 12 Maths Matrices PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 1 Relations and Functions Case Study Questions
• Chapter 2 Inverse Trigonometric Functions Case Study Questions
• Chapter 4 Determinants Case Study Questions
• Chapter 5 Continuity and Differentiability Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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Home > CBSE Class 12 Important Questions

Most Important Questions CBSE Class 12 Maths with Solutions

Cbse important questions for class 12 mathematics.

Mathematics improves the analytical and creative thinking of students and allows them to think differently. Concepts of class 12 Mathematics are directly asked in various competitive examinations like JEE and NDA. Therefore, it becomes really important for the students to have a good hold of the mathematical concepts.

At Educart, we provide our students with reliable resources so that they don’t get distracted from their journey and ace their examinations with flying colors.

In the table given below, we have provided the links to downloadable PDFs of chapter-wise important questions for class 12 Mathematics and that too for different categories of marks.

📈 Trending: Class 12 CBSE Syllabys 2024-25

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Benefits of CBSE Class 12 Mathematics Most Important Questions

A solid foundation in mathematics from classes 11 to 12 is necessary for students who wish to pursue careers in engineering research. Students can practice the associated questions by using NCERT books and appropriate study materials that help with idea clarification. The crucial questions for CBSE Class 12 Mathematics might aid in better comprehending the material and improve test preparation because the mathematics curricula for Classes 11 and 12 are extensive and divided into several areas and subtopics.

As per the updated CBSE Class 12 syllabus, the knowledgeable subject matter experts have compiled a list of all the crucial questions, broken down by chapter, along with clear explanations. To aid students in comprehending the questions stated and the intended responses, the explanations have been organized using a step-by-step approach. A variety of competency-based questions have been included, all while adhering to the most recent CBSE pattern. 

Why You Should Download CBSE Class 12 Mathematics Important Questions?

As exams start nearing, students try to adopt the best strategy to prepare for the exams to achieve good marks. Math is one of those subjects that give phobia mostly. To help students achieve the target, incorporating “Important Questions Practice” in the exam strategy is a vital step for many reasons.

• To have a deep understanding of topics in Class 12, understanding the topics from Class 12 will help in creating a strong base.
• These questions are curated to highlight the essential topics and principles and help students get the main idea behind that concept.
• Important questions provide extra help and work as important reference material to prepare well for exams.
• If any students want to appear for competitive exams like JEE, NEET, or any other exam, important questions will help in aligning with the exam pattern and strategy.
• You can curate a more effective study plan by shortlisting important topics.
• These questions will help you in boosting your confidence for the board exams.

CBSE Class 12 Important Questions will help students cover all the major topics and understand that chapter. At Educart, we have pledged to help students with the right material and help them in scoring their dream scores.

We hope that you practice the above important questions of mathematics and achieve your dream marks in it.

All the best! 

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• CBSE Maths Important Questions
• Class 12 Maths

CBSE Maths Class 12 Important Questions

CBSE Important Questions for Class 12 Maths provide you with chapter-wise strategies to prepare for the board examination. As we all know, CBSE Class 12 is one of the essential steps in career-making, and hence the marks obtained for Class 12 are accountable for admission to higher studies. Thus, we have focused on preparing you by providing you with different sets of questions that can be asked on your 12th board exam. Here, at BYJU’S, you will get Maths Class 12 CBSE important questions in PDF format so that you can download the files quickly and start practising.

Students can access the 12th Maths Important Questions along with the solutions and additional questions for practice. All these Class 12 Maths CBSE important questions will help the students score good marks in the board examination.

Also, check:

• Class 12 Maths Index
• CBSE Class 12 Maths Notes
• Class 12 Maths Formulas
• CBSE Class 12 Maths Revision Notes

The list of CBSE Important Questions for Class 12 Maths is as follows:

Practise more CBSE Class 12 Important Questions to understand the subject better. It will improve students’ problem-solving abilities, which is crucial for exam preparation. It will also increase the hold on each concept which is necessary to face the exams confidently.

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• CBSE Maths Class 12 Notes 2024-25
• Revision Notes

CBSE Maths Class 12 Notes for Effective Learning - Download Free PDF

CBSE Class 12 Maths Notes Chapter-wise 2024-25 is updated here in this article. We present a free-to-download PDF that comprises the chapter-wise Maths Notes Class 12 CBSE. Students can download the notes and use the same for their CBSE Class 12 Maths exam preparation.

In the study of Class 12 Mathematics , you will encounter varied formulae-based and theorem-based problem sums for which the related formulae and theorems must be within your grip, apart from this methodological concepts are also required to be kept in mind while doing the sums. Thus, no other study material  can be better than Class 12 Math Revision Notes for the same.

Detailed Overview of Maths Class 12 Notes

Cbse class 12 maths notes 2024-25 - chapter wise pdf for free.

In the table below we have provided the PDF links of all the chapters of CBSE Class 12 Maths Notes whereby the students are required to revise the chapters by downloading the PDF.

CBSE Class 12 Maths Weightage 2024-25

CBSE Maths Class 12 Notes must be studied smartly. Students must give priority to those chapters primarily that consist of major weightage of marks. Algebra, Calculus, Vectors, and Three-Dimensional Geometry are the most vital chapters from this perspective.  Check out the chapters with their marks distribution and prepare accordingly.

1000+ Basic Subjective Questions can be added advantage to your Class 12 Maths Notes

Vedantu provides a comprehensive set of basic subjective questions for Maths Class 12 Notes, with 1 mark and 2 marks subjective questions and answers. These questions are carefully curated by subject experts to ensure that they are relevant to the latest syllabus and exam patterns. They also cover a wide range of topics, so students can be sure to find questions that address their weak areas.

In addition to the questions, Vedantu class 12 maths notes also provides detailed answers, so students can learn how to answer them correctly. This helps students to understand the concepts behind the questions and to improve their problem-solving skills.

The basic subjective questions of class 12 math notes (1 mark & 2 mark) from Vedantu are a valuable resource for students who are preparing for their Class 12 Maths exams. They can help students to identify their weak areas, to improve their problem-solving skills, and to boost their confidence.

Subjective Questions benefits For Math Notes Class 12:

Relevant to the Latest Syllabus and Exam Patterns: Vedantu's basic subjective questions and Class 12 Maths notes are designed to align with the latest syllabus and exam patterns, ensuring that students focus on the most relevant topics and formats that they are likely to encounter in their Class 12 Maths Exams .

Coverage of Topics: Math Notes Class 12 covers a wide range of topics, allowing students to thoroughly practice and understand various concepts within the subject. This basic subjective questions coverage helps in developing a strong foundation in the subject matter.

Detailed and easy to understand Answers: Vedantu provides detailed solutions in Maths class 12 Notes, making it easier for students to grasp complex concepts and learn from their mistakes. 

Identification of Weak Areas: By referring to Vedantu's subjective questions and Maths 12 notes, students can identify their weak areas and specific topics that require further attention and improvement.

Improvement in Problem-Solving Skills: Regularly practicing 1 mark & 2 Mark questions along with Revision notes helps students to develop critical thinking and analytical skills.

Boosting Confidence: Subjective questions and Math Class 12 notes, helps to grow the confidence in the subject and it positively impacts their academic performance in exams.

If you are a student who is preparing for your Class 12 Maths exams, I highly recommend using Vedantu's Math Class 12 Notes with 1 mark and 2 mark subjective questions. They are a valuable resource that can help you to succeed in your exams.

CBSE Class 12 Maths Chapter Wise Revision Notes 2024-25 - Benefits of the Revision Notes

CBSE Class 12 Math Notes are prepared for some distinctive reasons. These reasons provide ample benefits that can be rendered by the CBSE Class 12 Maths students. Let us check from the following pointers what benefits can be enjoyed by the students by revising from Vedantu’s PDF notes:

Maths 12 Notes are sincerely made by the expert team at Vedantu to help the students gain more confidence for facing the exams, making the revision notes quite reliable to revise. 

The math notes class 12 are prepared with simple and lucid language; thus by referring these notes, the students can precisely have a clear and smooth understanding of Mathematics. 

We have highlighted the essential topics such as vectors, probability, relation, and functions, etc. through in-depth explanation with practice problems. This will give the students a clear understanding and good conceptual clarity will be attained by them.

Class 12 Mathematics is not only complicated but also important for students as it can determine their performance in board exams as well in other competitive exams, which affect their career. So, it is really important to have a better understanding of all the crucial topics of Class 12 Maths to perform better in all exams, and for that revision notes are of great help. Created under the guidance of expert faculty, CBSE Math notes Class 12 help all the students to cover the critical and high-weightage topics simply and efficiently without panicking and thus can improve their logical thinking, concepts and academic score up to a great extent.

CBSE Class 12 Maths Study Materials 2024-25

This was all for the CBSE Maths Class 12 Notes Chapter Wise 2024-25. The article aimed at introducing the CBSE Class 12 Maths Notes for students which will be quite beneficial for them in order to prepare appropriately for the exam. Since our experienced faculty makes these materials for students and teachers, it covers all the essential and complex topics simply and broadly. Students can avail of CBSE Math Notes Class 12 for a quick revision for themselves in PDF format from the official website. They can log in to the official website and get into the online tutoring sessions for better learning. 

FAQs on CBSE Maths Class 12 Notes 2024-25

1. Are There any Particular Features Provided to the Students for Mathematics Apart from the Syllabus by Vedantu?

Yes, following are some particular features provided in Vedantu Class 12 maths revision notes for students: 

Concise notes for complex topics help a fluidity of understanding.

Subject experts make the materials with decades of experience and knowledge of mathematics.

No hard sentences. Very easy and quick notes with in-depth knowledge.

Vedantu Experts provide all these features for the better learning and performance of students in complex subjects like Class 12 mathematics. With Class 12 revision notes, students can understand each topic quickly and clearly without any problems.

2. What are the Crucial Chapters in the Mathematics Syllabus for Class 12?

The latest syllabus for class 12 mathematics 2024-25 cover some crucial chapters and that is: 

Relations and Functions

Vectors and Three - Dimensional Geometry

Linear Programming

Probability

3. Is Chapter-Wise Revision Notes for Class 12 Maths Provided Online by Vedantu?

Indeed, Vedantu provides Revision Notes for Class 12 maths with chapter-wise solutions. They are well organized as well as cover all the critical topics in depth. They are available online in PDF format to download for free by both students and teachers. Ncert notes for class 12 maths are made by expert faculty who are experienced and reliable. Students should feel free to access these notes for better understanding and performance in exams.

4. How many chapters are present in Class 12 Maths?

Class 12 Mathematics textbook comprises a total of 13 chapters. All the chapters are significant from the board examination perspective. Hence, students should practice all these chapters extensively from their NCERT textbooks. They can also refer to NCERT Solutions offered by Vedantu. In addition to these solutions, Vedantu also offers revision notes, sample papers, and previous years' question papers for Class 12 students to practice. Vedantu provides all the mentioned services absolutely free to its students.

5. Which website is best for Class 12 Maths NCERT solutions?

Many online study portals have come up in the past few years. Owing to the pandemic, many students have turned to online help for their studies. However, too many choices end up confusing the students. The best websites produce authentic and quality content prepared by master professionals. Vedantu is one such website that aims at reimagining learning and teaching processes. The study material by Vedantu follows CBSE guidelines and is state of the art.

6. Is the NCERT textbook enough for Class 12 boards Maths?

NCERT forms the basis of the CBSE curriculum. For the Class 12 Maths board examination, the NCERT textbook is more than enough for you to score perfect marks in examinations. Most of the questions are asked directly from the NCERT textbook. Hence, you need to have exquisite and thorough preparation from the NCERT textbook. Additionally, you should solve as many sample papers and previous years’ question papers while preparing for board examinations. This should prepare you to score exceptionally well in the board exams.

7. Suggest some useful study tips for preparing for CBSE Class 12 Mathematics Board Examination.

To outshine in your CBSE class 12 mathematics board examination, here are some easy tips for you to follow:

Pay attention in class. In case of any doubt, refer it to your teacher at the earliest. Make sure your concepts are perfectly clear.

Familiarise yourself with the weightage of each unit and create a study plan accordingly.

Practice the NCERT textbook and its Solutions thoroughly.

Go over the revision notes, sample papers, and previous years’ question papers again and again.

8. Why do we need notes for Class 12 Maths?

Students often believe that they only need to practice the example and exercise questions from the NCERT textbook. They often do not read the chapter, which contains important explanations and definitions. Having revision notes for Class 12 Maths is beneficial in understanding the core concepts of the chapter along with all the important definitions, theorems, and formulas. Vedantu's revision notes make it easy to have all this significant information in one place for easy access and reference. The revision notes are also available on the Vedantu app.

9. What is the hardest chapter in math class 12?

Determining the absolute "hardest" chapter in math class 12 depends on individual strengths and weaknesses, but there are a few contenders typically seen as challenging:

1. Applications of Integrals (Chapter 8)

2. Three-Dimensional Geometry (Chapter 11)

3. Probability (Chapter 13)

4. Inverse Trigonometric Functions (Chapter 1)

Other chapters like Differential Equations (Chapter 9) and Vectors (Chapter 10) might also pose challenges depending on individual learning styles and preferences.

Revision Notes for Class 12

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CBSE Case Study Class 12

While preparing for the board exams, students are being judged on different levels of skills, such as writing, reading, etc. CBSE Case Study Class 12 questions are one of them that helps in assessing critical thinking.

The Central Board of Secondary Education will be asking the case study questions in the Class 12 board examination. Therefore, here on this page, we have provided the CBSE Case Study Class 12 for Maths, Physics, Chemistry, Biology and other subjects. Our subject matter experts have prepared Case Study questions so that Apart from the basic standard questions, students can have a variety of problems to solve. 

Just like MCQs, and other written types questions CBSE Case Study Class 12 questions will impact the overall performance of a student. Therefore for the convenience of the students we have provided the download links here, so that they can easily access the Class 12 Case Study.

Download Subject Wise CBSE Case Study Class 12 Question and Answers PDF 

There are three different streams in class 12th: Science, Arts & Commerce. And all these streams have a variety of subjects therefore, here our subject experts have crafted the Subject Wise Case Study For Class 12. Download Subject Wise CBSE Case Study Class 12 Question and Answers PDF from the below given links.

CBSE Case Study Questions Class 12 for Maths

To learn how to answer CBSE Case Study Class 12 maths questions, it would be a good choice to refer to the separate set of questions in PDF. CBSE Case Study Questions for Class 12 Maths can be quite useful and helpful in understanding how the board will prepare the case based questions for maths. 

The Maths Case studies are distributed into different chapters as per the prescribed syllabus of maths. Each and every chapter contains several number of case studies problems which enable the learners to gain in-depth knowledge in the subject.

The maths case study questions of class 12 are usually based on the formula. If any student wants to get a good score in maths case studies then they have to be well versed with a set of formulas as per the chapters and topics. Case Study Class 12 Maths can be downloaded here on this website for free of cost.

Case Study Questions Class 12 Chapter 1 Relations And Functions

Case Study Questions Class 12 Chapter  3 Matrices

Case Study Questions Class 12 Chapter  4 Determinants

Case Study Questions Class 12 Chapter  5 Continuity And Differentiability

Case Study Questions Class 12 Chapter  6 Application Of Derivatives

Case Study Questions Class 12 Chapter  8 Application Of Integrals

Case Study Questions Class 12 Chapter  9 Differential Equations

Case Study Questions Class 12 Chapter  10 Vector Algebra

Case Study Questions Class 12 Chapter  11 Three Dimensional Geometry

Case Study Questions Class 12 Chapter  12 Linear Programming

Case Study Questions Class 12 Chapter  13 Probability

CBSE Case Study Questions Class 12 for Physics

CBSE Class 12 Physics Case Study for different chapters can be interesting to solve. Class 12th physics case studies generally contain descriptive paragraphs and 4 to 5 different questions are given based on the paragraph. Students are required to read the paragraph thoroughly and understand them as well as observe the given data and information to answer the Class 12 Case Study Questions for Physics. 

In order to solve those questions students are required to have a better understanding of the basic level of physics concepts too, so make sure to use Class 12 Revision Notes of Physics. 

Case Study Questions Class 12 Chapter 1 Electric Charges and Fields

Case Study Questions Class 12 Chapter 2 Electrostatic Potential And Capacitance

Case Study Questions Class 12 Chapter 3 Current Electricity

Case Study Questions Class 12 Chapter 4 Moving Charges And Magnetism

Case Study Questions Class 12 Chapter 5 Magnetism And Matter

Case Study Questions Class 12 Chapter 6 Electromagnetic Induction

Case Study Questions Class 12 Chapter 7 Alternating Current

Case Study Questions Class 12 Chapter 8 Electromagnetic Waves

Case Study Questions Class 12 Chapter 9 Ray Optics & Optical Instruments

Case Study Questions Class 12 Chapter 10 Wave Optics

Case Study Questions Class 12 Chapter 11 Dual Nature Radiation & Matter

Case Study Questions Class 12 Chapter 12 Atoms

Case Study Questions Class 12 Chapter 13 Nuclei

Case Study Questions Class 12 Chapter 14 Semiconductor Electronics - Materials, Devices & Simple Circuits

CBSE Case Study Questions Class 12 for Chemistry

Students opted for Science stream will have to study CBSE Case Study Class 12 Chemistry. The given PDF of CBSE Class 12 Case Study Questions for Chemistry will enable the students to practice tons of questions on a regular basis. It will help them to revise the chemistry questions and its syllabus frequently. The Case study questions allow students to think more creative and find the answers in the quickest way possible. Links to download the PDF file of Class 12 Chemistry Case Study are given here.

Case Study Questions Class 12 Chapter 1 The Solid State

Case Study Questions Class 12 Chapter  2 Solutions

Case Study Questions Class 12 Chapter  3 Electrochemistry

Case Study Questions Class 12 Chapter  4 Chemical Kinetics

Case Study Questions Class 12 Chapter  5 Surface Chemistry  

Case Study Questions Class 12 Chapter  7 The p-Block Elements

Case Study Questions Class 12 Chapter  8 The d- and f-Block Elements

Case Study Questions Class 12 Chapter  9 Coordination Compounds

Case Study Questions Class 12 Chapter  10 Haloalkanes And Haloarenes

Case Study Questions Class 12 Chapter 11 Alcohols, Phenols And Ethers

Case Study Questions Class 12 Chapter  12 Aldehydes. Ketones & Carboxylic Acids

Case Study Questions Class 12 Chapter  13 Amines

Case Study Questions Class 12 Chapter 14 Biomolecules

CBSE Case Study Questions Class 12 for Biology

There are lots of chapters in class 12 Biology from which Class 12 Case Study Questions can be framed. Going through such types of questions help the students to assess their understanding level in the topics discussed in NCERT Class 12 Biology Books. By practicing the Class 12 Case Study Questions for Biology students will be very confident to ace the board exam. Also the Biology case study will be very useful for the NEET exam preparation.

Doing a regular practice of Class 12 Biology Case Study questions is a great way to score higher marks in the board exams as it will help students to develop a grip on the concepts. 

Case Study Questions Class 12 Chapter 2 Sexual Reproduction in Flowering Plants

Case Study Questions Class 12 Chapter 3 Human Reproduction

Case Study Questions Class 12 Chapter 4 Reproductive Health

Case Study Questions Class 12 Chapter 5 Principles of Inheritance & Variation

Case Study Questions Class 12 Chapter 6 Molecular Basic of Inheritance

Case Study Questions Class 12 Chapter 8 Human Health And Diseases

Case Study Questions Class 12 Chapter 10 Microbes in Human Welfare

Case Study Questions Class 12 Chapter 11 Biotechnology - Principles & Processes

Case Study Questions Class 12 Chapter 12 Biotechnology And Its Applications

Case Study Questions Class 12 Chapter 13 Organisms And Populations

Case Study Questions Class 12 Chapter 15 Biodiversity And Conversation

Case study types of questions are generally descriptive that helps to gather more information easily so, it is kinda easy to answer. However, our subject matter experts have given the solutions of all the CBSE Case Study Class 12 Biology questions.

Passage Based Class 12 Case Study Questions in PDF

CBSE Class 12 Case studies are known as Passage Based Questions. These types of problems usually contain a short/long paragraph with 4 to 5 questions. 

Students can easily solve Passage Based Class 12 Case Study Questions by reading those passages. By reading the passage students will get the exact idea of what should be the answers. Because the passage already contains some vital information or data. However a better understanding of the basic concepts that can be learned from the NCERT Class 12 Textbooks will aid in solving the Case based questions or passage based questions.

How to Download CBSE Case Study of Class 12?

Follow the below given simple steps to know how to download CBSE Case Study of Class 12:-

• Open Selfstudys website in your browser
• Go to the navigation menu that look like this
• Now, click on CBSE and then Case Study respectively
• A new page will open, where you have to click on “Class 12”
• Now, you are ready to select the subject for which you want to download the case study questions.

How to Solve Case Study Based Questions of Class 12?

There are very simple methods that a student should keep in mind while solving CBSE Case Study Class 12 for any subject:

• Read each line of paragraph carefully and pay attention to the given data/numbers. Often questions are framed according to the highlighted data of the passage.
• Since case study questions are often framed in Multiple choice questions, students should have the knowledge of elimination methods in MCQs.
• Having a good understanding of the topics that are discussed in CBSE Class 12 Books are ideal to Solve Case Study Based Questions of Class 12.

Features Of Class 12 Case Study Questions And Answers PDF

The three most noticeable features of Class 12 Case Study Questions And Answers Pdf are -

• It Is Free To Use:  Keeping in mind the need of students and to help them in doing Self Study, our team has made all the PDF of CBSE Case Study Class 12 free of cost.
• Answers Are Given:  Not only the PDFs are free provided but answers are given for all the questions of CBSE Case Study Class 12. 
• PDF Can Be Downloaded Or Viewed Online:  Many students don’t like to download the PDFs on their device due to the shortage of storage. Therefore, CBSE Class 12 Case Study questions are made available here in online format, so that students can view them online. However, through the Selfstudys app, a learner can download the PDFs too.

Benefits of Using CBSE Class 12 Case Study Questions and Answers

The CBSE Class 12 Case Study Questions and Answers can help a student in several ways:

• In Exam Preparation:  Those who go through the CBSE Case Study Class 12 will find support during the exam preparation as case based questions are also asked in the CBSE Class 12 Board examination. 
• Help in brushing up the previous learnings:  No matter how brilliant you are, you have to revise the studied topics time and again to keep them refreshed. And in this task, the CBSE Class 12 Case Study Questions and Answers can help a lot.
• To develop the critical thinking:  Able to analyse information and make an objective judgement is a skill that is known as critical thinking. A student of class 12 can use CBSE Case Study Class 12 with answers to develop critical thinking so that they can make better decisions in their life and in the board examination.

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CBSE Class 12 Board Result 2024 declared: Direct link and Toppers List Now Available

The CBSE (Central Board of Secondary Education) has announced the results for Class 10th and 12th in 2024 today, 13th May 2024. This year, 87.98% of students passed the Class 12th exams. If you took the exams, you can check your marks on official websites like results.cbse.nic.in , cbse.gov.in , or cbseresults.nic.in . This article provides a direct link to the results page and a detailed guide on how to access the results.

CBSE Class 12th Result 2024 Declared

CBSE 12th Class Result 2024: Check Your Scores Now at cbse.gov.in

The CBSE Class 10 exams were held from February 15 to March 13 , while the Class 12 exams took place from February 15 to April 2, 2024. Around 39 lakh students from 26 countries participated in these exams. In Delhi alone, 5.80 lakh students appeared for the CBSE Board exams in 2024. Notably, CBSE has decided to stop publishing merit lists to reduce unhealthy competition among students. Students can access their CBSE Class 12th results through the UMANG app, Digilocker app, Pariksha Sangam portal, or SMS service.

How to Download CBSE Class 12th Result 2024

The Central Board of Secondary Education (CBSE) has declared the Class 12 results today, May 13. Students can now check their results online on mobile or PC. Here’s the step-by-step procedure to download the CBSE Class 12th Result 2024,

Step 1: Visit the official website of CBSE at cbseresults.nic.in.

Step 2: on the homepage, click on the class 12th result link, step 3: log in using your credentials such as registration number and date of birth, step 4: the result will be displayed on the screen, step 5: download and take a printout of the result for future references, websites to check cbse 12th result 2024.

• Direct Link I
• Direct Link II
• Direct Link III

CBSE Class 12th Result 2024: Details Mentioned on Your Scorecard

• Name of student
• Exam details
• Parents name
• School name
• Date of birth
• City and state
• Education board name
• Subject wise marks
• Total marks
• Status- pass/fail

CBSE Class 12th Toppers List 2024

The Central Board of Secondary Education (CBSE) today announced the class 12 board results. CBSE Class 12 students can now check their much-awaited mark sheet on the board’s official website CBSE i.e., cbse.gov.in. Apart from the official website, the CBSE Class XII results will be available on the Umang mobile app, DigiLocker, and the IVRS system. The CBSE results were declared on May 12th last year. This year, the overall pass rate stands at 87.98%.

The CBSE has stated not to publish a Toppers List for the Class 12th Exams 2024. Instead, alongside the CBSE Class 12th Result 2024, the board will provide details such as the overall pass percentage, and results categorized by gender, school, and region, among others.

CBSE Class 12th Toppers List 2024: District Wise List

Notably, Trivandrum district achieved the highest pass rate, while Prayagraj ranked lowest. Here’s the Region-wise table for Pass Percentage in 2024:

CBSE Class 12 Result 2024: Girls Outshine Boys Once Again

Girls have once again outperformed boys, with 81.12% of boys and 91.52% of girls passing the exam, marking a 6.40% difference. Out of 16.33 lakh students registered, 16.21 lakh students have successfully passed the exam, reflecting an improvement in pass percentage as compared to the previous year.

In the end, Congratulations to the CBSE Class XII students of 2024! This marks the end of an important chapter and the exciting beginning of your next adventure. We hope this article helped you easily access your results and celebrate the toppers’ achievements. Best wishes for your future endeavors!

FAQs – CBSE Class 12th Result 2024 Out

Is the cbse class 12th result declared.

Yes, CBSE released the result of class 12th on the 13th of May i.e., today. Read the above article to know about the updates and changes in the result.

Is the CBSE class 12th result 2024 declared?

Yes, the CBSE Class 12th Result 2024 is declared now. Students can check their results on the official website of CBSE or Digilocker app or the Umang App.

Who is the topper in Class 12 CBSE 2024?

Read the full article to know about the topper and toppers list of CBSE Class 12th result 2024.

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Class 11 Maths NCERT Solutions: Step-by-Step NCERT Solutions Pdf

Class 11 Maths NCERT Solutions provide clear explanations for all questions in the NCERT textbooks used by the Central Board of Secondary Education (CBSE). We offers these solutions chapter-wise to help students understand the concepts and clear your any doubts. You can download Class 11 Maths NCERT Solutions in PDF format to study offline.

Using these NCERT Solutions helps students get ready for final exams by practicing different types of questions from the book. Our experts have designed these solutions in an easy-to-follow format to teach the best ways to solve problems and understand the concepts. Students should practice the problems in the CBSE Class 11 Maths textbook to prepare for exams and build a strong foundation for future classes.

Table of Contents

Class 11 Maths NCERT Solutions Download Pdf

The NCERT Solutions for Class 11 Maths, designed by math experts, are based on extensive research on each concept. These solutions are available in PDF format for free download, helping students efficiently learn and clear their doubts outside class hours. The solutions are provided in both chapter-wise and exercise-wise formats to aid thorough preparation for exams.

These solutions follow the NCERT textbook prescribed by the CBSE board. PDFs of the solutions can be downloaded for free. Every problem is solved accurately, considering the marks weightage.

Benefits of Practising Class 11 Maths NCERT Solutions

Class 11 Maths NCERT Solutions are excellent resources for students preparing for exams. These NCERT Class 11 Maths Solutions enhance understanding of concepts and improve problem-solving abilities. Here are some benefits of using ybstudy Class 11 Maths NCERT Solutions:

• These solutions provide a deep understanding of class 11 Maths syllabus .
• They enhance your logical thinking and problem-solving skills.
• They clarify your doubts and teach how to frame answers correctly.
• Practicing with NCERT Class 11 Maths Solutions helps in revising and preparing for exams, leading to higher scores.
• Students benefit from detailed explanations and step-by-step instructions.
• These Class 11 Maths NCERT Solutions boost students’ confidence.
• Regular practice with these Class 11 Maths NCERT exercises improves time management skills.

CBSE Class 11 Mathematics Syllabus 2024-25

How to prepare for ncert class 11 maths.

Preparing for Class 11 Mathematics requires a thorough understanding of concepts, robust problem-solving skills, and consistent practice. By following the below structured strategy, maintaining the right mindset, and putting in dedicated effort, you can significantly increase your chances of success in Class 11 Maths Preparation.

Step-by-Step Strategy for Preparing for Class 11 Mathematics

• Start with the Basics: Ensure a solid foundation in fundamental mathematics concepts. Clear basics help in solving complex problems efficiently. Understand where and how to apply specific concepts or approaches.
• Analyze the Syllabus: Divide the syllabus into five main sections: Algebra, Trigonometry, Calculus, Vectors & 3D Geometry, and Coordinate Geometry. Each section requires a tailored approach.

Section-Wise Strategy:

• Algebra: This large section tests your thinking ability more than formula memorization. Practice a variety of problems in Permutations and Combinations (PnC) and Probability to develop problem-solving skills. Complex Numbers, Matrices, Determinants, and the Binomial Theorem require perseverance to solve thoroughly. Focus on easier chapters for quick scores, such as Quadratic Equations, Sequence and Series, and Logarithms.
• Trigonometry: Easier and scoring, as questions are mostly formula-based. Master the application of trigonometric formulas to achieve desired results.
• Calculus: The most weighted section in Mathematics. Extensive practice is essential. As you practice more, you’ll start enjoying Calculus, and questions will become more manageable.
• Vectors and 3D Geometry: Vectors involve algebraic manipulations. 3D Geometry requires good spatial imagination. Though questions are often straightforward, they can be lengthy.
• Coordinate Geometry: This section involves numerous formulas and properties. Focus on finding the shortest approach to problems rather than relying solely on logic. Familiarize yourself with the attached complete formula list to aid in quick problem-solving.
• Practice Regularly: Solve problems from various sources: previous years’ question papers, mock tests, and study materials. Regular practice enhances problem-solving skills and boosts confidence.
• Use the Right Books: Stick to one publication and solve it multiple times.
• Analyze Your Mistakes: After solving problems, review your mistakes to understand where you went wrong. This reflection helps in avoiding similar mistakes and improves problem-solving skills.
• Develop a Problem-Solving Strategy: Adopt a systematic approach: break down complex problems into smaller parts, identify key concepts and formulas, and always verify your answers.
• Manage Your Time: Effective time management is crucial. Practice solving problems within the allotted time to enhance speed and accuracy.
• Stay Motivated: Maintain motivation and focus throughout your preparation. Take breaks, indulge in hobbies, and stay positive to manage stress effectively.

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CBSE Class 9 Artificial Intelligence Syllabus 2024-25 Unit Wise Weightage: Download The PDF For Free

Cbse class 9 artificial intelligence syllabus 2024-2025: artificial intelligence is an important subject that students must study to get a basic understanding of how ai works in this modern world. the central board of secondary education has released the latest curriculum for class 9 students for the academic year 2024-25. keep reading the article to learn about the syllabus. .

OBJECTIVES OF THE COURSE:

• To become AI-ready, Help learners understand the world of Artificial Intelligence and its applications through games, activities and multi-sensorial learning.
• Introducing the learners to three domains of AI in an age-appropriate manner.
• Allowing the learners to construct the meaning of AI through interactive participation and engaging hands-on activities.
• Revisiting AI domains, project cycle and Ethics
• Introducing the learners to the importance of Math for AI, data literacy and generative AI
• Introducing the learners to programming skills - Basic Python coding language.

CBSE Class 9 Artificial Intelligence Syllabus 2024-25

NOTE: D etailed curriculum/ topics covered under Part A: Employability Skills can be downloaded from the CBSE website.

• Unit 1: AI Reflection, Project Cycle and Ethics
• Unit 2: Data Literacy
• Unit 3: Math for AI (Statistics & Probability)
• Unit 4: Introduction to Generative AI
• Unit 5: Introduction to Python

UNIT 1: AI REFLECTION, PROJECT CYCLE AND ETHICS

Unit 2: data literacy, unit 3: math for ai (statistics & probability), unit 4: introduction to generative ai:, part-c: practical work , unit 5: introduction to python: suggested program list, part-d: project work / field visit / student portfolio.

Students can download the direct link for the syllabus from the link provided below. Happy Learning! For more such content, keep following Jagran Josh. 

CBSE Class 9 Artificial Intelligence Latest Syllabus FREE PDF Download

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CBSE Class 9 Information Technology Latest Syllabus 2024-25 Marking Scheme: Download The PDF For Free!

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